Why don't light emitters reflect light?
This is expected behavior for Cycles and in line with the way a physically based render engine is supposed to work.

By assigning a purely emission shader to a surface you are telling the render engine that that surface has no other light path component interaction, and is only emitting photons, no light is absorbed, no light is reflected, no light is refracted.

If you expect more light path behaviors from said surface you have to add the corresponding shaders for those.

What this means is practically you have to use a Mix shader to mix the emission with other materials cabale of reflecting light from other sources, in this case a simple Diffuse or Glossy shader will do.

For clarity sake the "strong light" is red colored and the weaker one is blue in my scene.



Also as mentioned by Cegaton, you don't specifically need those boxes, if your only intent is to stop light. You can either use actual Lamp objects set to Area which will by default only emit light in one direction, or use a node setup similar to the one below to limit a certain shader to the front facing geometry only.